Multiple Choice
Which of the following pairs of angles are coterminal angles in standard position?
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1. Measuring Angles
Angles in Standard Position
Multiple Choice
Which of the following angle measures in degrees are coterminal with in standard position?
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B
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D
Verified step by step guidance1
Recall that two angles are coterminal if they differ by a full rotation, which is 360 degrees. This means if you add or subtract multiples of 360° to an angle, you get angles coterminal with it.
Start with the given angle, 45°, and find angles coterminal by adding 360°: \(45^\circ + 360^\circ = 405^\circ\).
Next, find coterminal angles by subtracting 360°: \(45^\circ - 360^\circ = -315^\circ\).
Check the other given angles to see if they can be expressed as \(45^\circ \pm 360^\circ \times k\) where \(k\) is an integer. For example, 225° is not coterminal because \$225 - 45 = 180$, which is not a multiple of 360.
Conclude that the angles coterminal with 45° from the given options are those that can be written as \(45^\circ \pm 360^\circ\), specifically \(-315^\circ\) and \(405^\circ\).
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